The Incompressible Limits of Compressible Navier-Stokes Equations in the Whole Space with General Initial Data

It is showed that,as the Mach number goes to zero,the weak solution of the compressible Navier-Stokes equations in the whole space with general initial data converges to the strong solution of the incompressible Navier-Stokes equations as long as the later exists.The proof of the result relies on the new modulated energy functional and the Strichartz's estimate of linear wave equation.